The material of the last  three weeks corresponds to topics from Variational Calculus and Complex Analysis. In particular, the 12th week we will focus on  problems whose solution is based on the study of functionals defined on certain spaces of functions. We will meet notions as minimum principle, critical points of functionals, variation of functionals,  classical variational problems, Euler-Lagrange equations, and other. 

 In the BG book this week corresponds to  the third section of Chapter 9, with title ``Remarks on variational calculus'',  from the paragraph 9.3.1  to the end of  the paragraph 9.3.4, and includes the following concepts:

1) The notion of functionals;

2) Simple examples of variational problems;

3) The Lagrangian of variational problems;

4) Critical points of functionals;

5) The variation of functionals.